~It would not have been possible.
The bulk of the war was contested between Germany and the USSR. The end was written at Moscow, Leningrad and Stalingrad, long before the first US troops set foot in North Africa in November 1942 against the Vichy French and then the Italians and long after the Wehrmacht had spent all of six weeks in conquering France and sending the British Expeditionary Force scurrying back to the Isles. In fact, if Hitler had not succumbed to the pleas of his generals and halted the tanks to allow the infantry to catch up with them, the BEF would have been trapped at Dunkirk and the "miracle" evacuation would never have occurred. At Moscow, Army Group Central was crushed. After Stalingrad, Army Group South ceased to exist. Army Group North was stalemated at Leningrad and would remain so until the counter-attack that would quarantine it in the Courland Pocket and effectively remove it from the war.
Rome was finally occupied by the Western allies on June 4, 1944 (but the German 10th Army escaped). Southern Italy had never been of much importance to the OKW, which is why Kesselring had so few and such poorly trained and equipped troops (well, that and the cream of the Heer Army had long since been buried on the Eastern Front) and why he was not reinforced. The Western Allies were not even close to taking northern Italy or trying to cross the Alps. By comparison to the battles in the east, Normandy was a minor skirmish. Rommel and von Rundstedt had about 1 million troops with which to defend and occupy all of Western Europe. Of them, about 250,000 were within striking distance of the invasion beachheads and half of those had to be held in reserve to meet the real invasion, which was expected at Calais. The troops in Western Europe included old men, young boys and veterans declared unfit for duty in the east. Many were sent to the line without training and often without weapons. Entire units were composed of transcripts from occupied territories in the east who could not speak German and who could not communicate with their superiors during battle. By contrast, battles in the east often saw Heer Army forces of one million strong squaring off against Red Army forces of comparable or larger size, sometimes in contemporaneous battles.
Stalin would accept only unconditional surrender. The US and UK had to try to stay in the war until that happened in order to have any say as to the look of the post-war world. Hitler would never have offered surrender to Stalin, knowing full well what his fate and that of Germany would have been. The US and UK could not have accepted a surrender without Stalin's blessing and consent, for fear of risking war with the USSR. As Churchill told Hitler in 1941, the only force on the planet that could take on Germany in a war on the Continent and hope to survive, forget win, was the Red Army. History proved Churchill correct. Things hadn't changed much by 1944 except the Red Army had grown stronger, battle-tested and tough, and Soviet weaponry had improved. Given the numbers and logistics, not to mention the skirmish still taking place in the Pacific, there was no way the US and UK could take the chance of Stalin unleashing the T-34s and Yaks across Europe.
Eisenhower never planned to occupy Berlin. The Western allies had long since decided to let the Germans and Soviets bleed each other dry and to destroy each other. The Western hope was to negotiate an acceptable peace with Stalin over the fate of Germany and Europe, and the terms had pretty much been agreed on at Yalta and Tehran. Going back on the European question would have nullified the agreements concerning Japan and Asia.\
Perhaps with an earlier surrender, more ranking Nazis could have been induced to come to the US in programs like Operation Paperclip. As it was, we got Wernher von Braun and his brother and were able to build the Redstone Rockets on which to mount our nukes and the Saturn V launch vehicle that sent Apollo to the moon, and we got Hubertus Strughold, NASA's "Father of Space Medicine" who began his work with medical experiments at Dachau, not to mention Klaus "the Butcher of Lyon" Barbie and his fellow gestapo cronies of the Gehlen Organization who became the heart of CIA operations in East Germany and in Eastern Europe.
A more rational question might be "What would have happened if Hitler's hope that the UK and the US understoodd that Stalin and communism were common enemies and a common threat and joined in the alliance that Hitler believed would inevitably be forged until his final hours in the Fuhrerbunker?"